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      <a id="modulus"></a>
      <div class="titlepage"></div>
      <a id="IndexPercent" class="indexterm"></a>
      <div class="refnamediv">
        <h2>
          <span class="refentrytitle">%</span>
        </h2>
        <p>% — 
      Modulus operator.
          </p>
      </div>
      <div class="refsect1">
        <a id="idp87595056"></a>
        <h2>Description</h2>
        <p>
      Arithmetic operators perform operations of change-sign (negate), don't-change-sign, logical AND logical OR, add, subtract, multiply and divide. Note that a value or an expression may fall between two of these operators, either of which could take it as its left or right argument, as in
      </p>
        <div class="literallayout">
          <p>a + b * c.</p>
        </div>
        <p>
    </p>
        <p>
      In such cases three rules apply:
    </p>
        <p>
      1. * and <span class="emphasis"><em>/</em></span> bind to their neighbors more strongly than + and −. Thus the above expression is taken as
      </p>
        <div class="literallayout">
          <p>a + (b * c)</p>
        </div>
        <p>
      with * taking b and c and then + taking a and b * c.
    </p>
        <p>
      2. <span class="emphasis"><em>+</em></span> and <span class="emphasis"><em>−</em></span> bind more strongly than &amp;&amp;, which in turn is stronger than ||:
      </p>
        <div class="literallayout">
          <p>a &amp;&amp; b - c || d</p>
        </div>
        <p>
      is taken as
      </p>
        <div class="literallayout">
          <p>(a &amp;&amp; (b - c)) || d</p>
        </div>
        <p>
    </p>
        <p>
      3. When both operators bind equally strongly, the operations are done left to right:
      </p>
        <div class="literallayout">
          <p>a - b - c</p>
        </div>
        <p>
      is taken as
      </p>
        <div class="literallayout">
          <p>(a - b) - c</p>
        </div>
        <p>
    </p>
        <p>
      Parentheses may be used as above to force particular groupings.
    </p>
        <p>
      The operator <span class="emphasis"><em>%</em></span> returns the value of <span class="emphasis"><em>a</em></span> reduced by <span class="emphasis"><em>b</em></span>, so that the result, in absolute value, is less than the absolute value of <span class="emphasis"><em>b</em></span>, by repeated subtraction. This is the same as modulus function in integers. New in Csound version 3.50.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp87610144"></a>
        <h2>Syntax</h2>
        <pre class="synopsis">a <span class="command"><strong>%</strong></span> b  (no rate restriction)</pre>
        <p>
      where the arguments <span class="emphasis"><em>a</em></span> and <span class="emphasis"><em>b</em></span> may be further expressions.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp87613824"></a>
        <h2>Arguments</h2>
        <p>
      The arguments of % can be scalar values or k-rate one
      dimensional arrays (vectors), or any combination.  If one of the
      arguments is an array, so is the value.
    </p>
      </div>
      <div class="refsect1">
        <a id="idp87615296"></a>
        <h2>Examples</h2>
        <p>
      Here is an example of the % operator. It uses the file <a class="ulink" href="examples/modulus.csd" target="_top"><em class="citetitle">modulus.csd</em></a>.
      </p>
        <div class="example">
          <a id="idp87617072"></a>
          <p class="title">
            <strong>Example 20. Example of the % operator.</strong>
          </p>
          <div class="example-contents">
            <p>See the sections <a class="link" href="UsingRealTime.html" title="Real-Time Audio"><em class="citetitle">Real-time Audio</em></a> and <a class="link" href="CommandFlags.html" title="Csound command line"><em class="citetitle">Command Line Flags</em></a> for more information on using command line flags.</p>
            <pre class="programlisting">
<span class="csdtag">&lt;CsoundSynthesizer&gt;</span>
<span class="csdtag">&lt;CsOptions&gt;</span>
<span class="comment">; Select audio/midi flags here according to platform</span>
-odac -Ma --midi-key=4 --midi-velocity-amp=5 -m0  <span class="comment">;;;realtime audio out and midi in</span>
<span class="comment">;-iadc    ;;;uncomment -iadc if realtime audio input is needed too</span>
<span class="comment">; For Non-realtime ouput leave only the line below:</span>
<span class="comment">; -o %.wav -W ;;; for file output any platform</span>
<span class="csdtag">&lt;/CsOptions&gt;</span>
<span class="csdtag">&lt;CsInstruments&gt;</span>

<span class="ohdr">sr</span> <span class="op">=</span> 44100
<span class="ohdr">ksmps</span> <span class="op">=</span> 32
<span class="ohdr">nchnls</span> <span class="op">=</span> 2
<span class="ohdr">0dbfs</span>  <span class="op">=</span> 1

giScale <span class="ohdr">ftgen</span> 1, 0, <span class="op">-</span>12, <span class="op">-</span>2, 0, <span class="op">-</span>34, <span class="op">-</span>7, 10, <span class="op">-</span>14, 3, <span class="op">-</span>21, <span class="op">-</span>3, <span class="op">-</span>27, <span class="op">-</span>10, 7, <span class="op">-</span>17	<span class="comment">;12 note scale with detuned keys</span>

<span class="oblock">instr</span> 1

ikey	<span class="op">=</span> p4
ivel	<span class="op">=</span> p5
indx	<span class="op">=</span> ikey <span class="op">%</span> 12								<span class="comment">;work on the twelftone scale</span>
icent	<span class="opc">tab_i</span> indx, giScale							<span class="comment">;load the scale</span>
ifreqeq	<span class="op">=</span> <span class="opc">cpsmidinn</span>(ikey)
ifreq	<span class="op">=</span> ifreqeq <span class="op">*</span> <span class="opc">cent</span>(icent)							<span class="comment">;change frequency by cents from table</span>
<span class="opc">prints</span>	"Key <span class="op">%</span>d modulus 12 <span class="op">=</span>  <span class="op">%</span>d. ", ikey, indx
<span class="opc">prints</span>	"Equal<span class="op">-</span>tempered frequency of this key  <span class="op">=</span> <span class="op">%</span>f,", ifreqeq
<span class="opc">prints</span>  " but here with <span class="opc">cent</span> deviation <span class="op">%</span>d <span class="op">=</span> <span class="op">%</span>f<span class="op">%</span>n", icent, ifreq
asig	<span class="opc">vco2</span> ivel<span class="op">*</span>.5, ifreq
	<span class="opc">outs</span> asig, asig

<span class="oblock">endin</span>
<span class="csdtag">&lt;/CsInstruments&gt;</span>
<span class="csdtag">&lt;CsScore&gt;</span>
<span class="stamnt">f</span> 0 60		<span class="comment">;run for 60 seconds</span>

<span class="stamnt">e</span>
<span class="csdtag">&lt;/CsScore&gt;</span>
<span class="csdtag">&lt;/CsoundSynthesizer&gt;</span>
</pre>
          </div>
        </div>
        <p><br class="example-break" />
    </p>
      </div>
      <div class="refsect1">
        <a id="idp87621088"></a>
        <h2>See Also</h2>
        <p>
      <a class="link" href="subtracts.html" title="-"><em class="citetitle">-</em></a>, 
      <a class="link" href="adds.html" title="+"><em class="citetitle">+</em></a>, 
      <a class="link" href="opand.html" title="&amp;&amp;"><em class="citetitle">&amp;&amp;</em></a>, 
      <a class="link" href="opor.html" title="||"><em class="citetitle">||</em></a>, 
      <a class="link" href="multiplies.html" title="*"><em class="citetitle">*</em></a>, 
      <a class="link" href="divides.html" title="/"><em class="citetitle">/</em></a>, 
      <a class="link" href="raises.html" title="^"><em class="citetitle">^</em></a>
    </p>
      </div>
      <div class="refsect1">
        <a id="idp87628928"></a>
        <h2>Credits</h2>
        <p>Arithmetic on vectors is new in version 6.00</p>
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